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If xhyk is an integrating factor of the differential equation y(1 + xy) dx + x(1 — xy) dy = 0, then the ordered pair (h, k) is equal to
  • a)
    (−2, −2)
  • b)
    (−2, −1)
  • c)
     (−1, −2)
  • d)
    (−1, −1)
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
If xhyk is an integrating factor of the differential equation y(1 + xy...
If xh yk is an I.F. of differential equation, Then given equation become exact differential equation.
xh uk+1 (1 + xy)dx + xh +1 yk (1 – xy) dy = 0
So

=> (k + 1)ykxh + (k + 2)xh + 1yk + 1
= (h + 1)xhyk - (h + 1)xk + 1yk + 1
Comparing coefficients of both the sides, we have
h – k = 0
h + k – 4
⇒ h = –2, k = – 2
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Most Upvoted Answer
If xhyk is an integrating factor of the differential equation y(1 + xy...
It seems like the question is incomplete as there is no given equation after "x(1". Please provide the complete equation so that I can assist you further.
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If xhyk is an integrating factor of the differential equation y(1 + xy) dx + x(1 — xy) dy = 0, then the ordered pair (h, k) is equal toa)(−2, −2)b)(−2, −1)c)(−1, −2)d)(−1, −1)Correct answer is option 'A'. Can you explain this answer?
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